## ParthKohli one year ago two numbers are randomly chosen from 1, 3, 5, 7, ..., 145, 147, 149

1. ParthKohli

in how many ways can they be chosen so that we have their product divisible by 5?

2. ParthKohli

Total numbers: 75. Numbers divisible by 5: 15. Case-I: One number and only one number of the two chosen ones is divisible by 5. $$15$$ numbers divisible by 5 and $$60$$ numbers that are not. Thus there are $$15\cdot 60= 900$$ such pairs. Case-II: Both numbers divisible by 5.$\binom{15}{2}=105$Total numbers: 1005.

3. ParthKohli

The given answer is 1020. Am I missing something?

4. mathmath333

$$\color{white}{bookmark}$$

5. ParthKohli

oooh, goddammit. you know what, the original question has a list that goes up to 151 :P

6. ParthKohli

in that case, divisible by 5: 15... total: 76

7. ParthKohli

so I'm right in a way. I just read the list till 149 lol